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Transcript
PHYS 410:
Computational Physics
Term 2 – 2008/09
What is "computational physics"?
1. Process and analyse large amounts of data from measurements;
fit to theoretical models; display and animate graphically
Ex: search for "events" in particle physics, image analysis in
astronomy.
2. Numerical solution of equations that cannot be accomplished by
analytical techniques (coupled, nonlinear etc.)
Ex: fluid dynamics (Navier Stokes), numerical relativity
(Einstein's field equations), electronic ground state
wavefunctions in solid state systems, nonlinear growth equations
3. Computer "experiments": simulate physical phenomena, observe
and extract quantities as in experiments, explore simplified
model systems for which no solution is known.
Ex: molecular simulations of materials, protein folding,
planetary dynamics (N-body dynamics).
Theory - Computation - Experiment
Computational Physics
Performs idealized
"experiments" on the
computer, solves physical
models numerically
predicts
Theoretical Physics
Construction and
mathematical (analytical)
analysis of idealized
models and hypotheses
to describe nature
tests
Experimental Physics
Quantitative measurement
of physical phenomena
Computation across all areas of physics
• High Energy Physics: lattice chromodynamics, theory of the
strong interaction, data analysis from accelerator experiments
• Astronomy and Cosmology: formation and evolution of solar
systems, star systems and galaxies
• Condensed Matter Physics:
- electronic structure of solids and quantum effects
- nonlinear and far from equilibrium processes
- properties and dynamics of soft materials such as polymers,
liquid crystals, colloids
• Biophysics: simulations of structure and function of
biomolecules such as proteins and DNA
• Materials Physics: behavior of complex materials, metals,
alloys, composites
Example 1: Biophysics
Chymotrypsin Inhibitor 2
314,000 atom simulation at UIUC
Example 2: Materials Physics
• Glassy polymers (eg.
PMMA, plexiglass)
consist of long chain
molecules
• Under load, the polymer
forms a dense network of
fibrils and voids that is
controlled by the
molecular level chain
structure
• This process makes them
"tough" to break and
therefore useful materials
Molecular dynamics simulation
of fracture in glassy polymers
Example 3: Materials Physics
Dislocation dynamics with a billion copper atoms at LLNL
Example 3: Materials Physics
Crack propagation in Silicon
Modeling materials on
different length scales:
• quantum mechanics
(tight binding)
• classical forces
(molecular dynamics)
• continuum mechanics
(finite element)
http://cst-www.nrl.navy.mil/~bernstei/projects/nb.html
Example 4: Materials Physics
Phase field models of dendrite growth
• Directional solidfication in a binary alloy
• Numerical solution of a PDE
 t   W (n ) 2     3  U (1   2 ) 2
• Phase field (order parameter) describes liquid/solid
• critical nucleus
growing into an
undercooled melt
• adaptive mesh
refinement
http://mse.mcmaster.ca/faculty/provatas/solid.html
Example 5: High Energy Physics
LHC
• Particle colliders such as the LHC at
CERN in Geneva are unraveling the
interactions between fundamental particles
• These experiments produce large amounts
of data that is analyzed worldwide
(including here at UBC) using GRID
computing
High Energy Physics group @ UBC
How is it done?
• "Small simulations" on workstations such as this laptop
Program with numerical packages such as
Maple/Matlab/Mathematica or in high-level programming
languages such as C/C++ or Fortran
• "Large simulations" on compute clusters or supercomputers
may require lots of memory or calculation time
distribute the problem over many (~10 to 100) processors
either separately or "in parallel"
• Grid computing: networks of supercomputing centers
dedicated to scientific problems, spatially separated
How does the computational physicist
work?
• Devise and implement a computer model for the physical
question of interest
• Needs numerical mathematics toolkit: discretization, error
analysis, stability, efficiency
• Perform the computation
• Analyse and visualize the data
• Interpret and compare to experiment and theory
• Improve model predictions
Exciting research opportunities
• In computer simulations we can study more realistic physical
models, but still have full control over the degree of complexity.
• Enables quantitative predictions
• In Condensed Matter/Materials Physics an important goal is to
be able to predict material behavior:
Can we design new materials, new substances, new drugs etc.
on the computer?
To achieve this goal, we need techniques that span the length
and time scales from the atomistic (femtometers/seconds) to the
scales we use in everyday life (say seconds/centimeters).
This is not easy; this research effort is called
"multiscale modeling"
Outline of the course
• Introduction to UNIX/LINUX
• Introduction to programming and compiling in C
• Data visualization
• Ordinary differential equations in physics:
kinematics, oscillatory motion and chaos, orbital motion
• Partial differential equations in physics
electrostatics, wave equation, diffusion
• Stochastic Methods
Random walks, fractals and percolation, Monte Carlo
• Quantum systems
Schrödinger equation, ground state energy and wavefunctions,
wavepackets
How to get started?
• Get an account on the departmental UNIX system by selfregistering in HENN 205
• Familiarize yourself with the environment (if new to you)
• Get material from the course webpage
www.phas.ubc.ca/~jrottler/teaching/410/onres.html
and practice basic operations such as file manipulation, text
editors, remote logins as demonstrated in class
• Experiment with basic C programming constructs, learn how to
compile and run code
• Learn how to plot numerical data and functions using your
favorite software. One possibility: gnuplot
 now we are ready to start doing real computational physics!
Introduction to UNIX/LINUX
•
•
•
•
•
Files and directories
Basic commands
Manipulating files
Working with the "shell"
Basic shell programming
please see also the notes by Prof. M. Choptuik:
laplace.physics.ubc.ca/410/Notes_unix.html